Q1
What is an arithmetic progression?
AA sequence with a constant common difference
BA sequence with no pattern
CA sequence that always decreases
DA sequence with random differences
SSCClass 10 (SSC)Mathematics - Algebra (बीजगणित)Ch 3 · Topic 1
Arithmetic Progression
An arithmetic progression (AP) is a sequence where each term increases or decreases by a constant amount, called the common difference.
Core concept
The nth term of an AP is calculated as aₙ=a+(n-1)d, where a is the first term, n is the term number, and d is the common difference.
How it works
The sum of the first n terms of an AP is Sₙ=n/2×[2a+(n-1)d], useful for quickly finding totals without adding each term.
Why it matters
An AP can be identified by checking if the difference between consecutive terms remains constant throughout the sequence.
Key detail
Arithmetic progressions have real-life applications, like calculating regular savings growth, seating arrangements, or simple interest calculations.
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Quick notes
• AP: each term changes by a constant amount.
• nth term: aₙ=a+(n-1)d.
• Sum of n terms: Sₙ=n/2×[2a+(n-1)d].
• Common difference must stay constant.
• This identifies a sequence as an AP.
• Real-life uses: savings growth, seating.
• AP formulas avoid manual term-by-term addition.
• Practice builds AP problem-solving skills.